Solve for $x$ and $y$ using elimination. ${-2x+2y = 2}$ ${2x+5y = 33}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $7y = 35$ $\dfrac{7y}{{7}} = \dfrac{35}{{7}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-2x+2y = 2}\thinspace$ to find $x$ ${-2x + 2}{(5)}{= 2}$ $-2x+10 = 2$ $-2x+10{-10} = 2{-10}$ $-2x = -8$ $\dfrac{-2x}{{-2}} = \dfrac{-8}{{-2}}$ ${x = 4}$ You can also plug ${y = 5}$ into $\thinspace {2x+5y = 33}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(5)}{= 33}$ ${x = 4}$